Tunneling wave function of the universe

TL;DR

This paper compares three methods for defining the tunneling wave function of the universe within a de Sitter minisuperspace model with a scalar field, showing they produce consistent results and well-behaved fluctuations.

Contribution

It demonstrates the equivalence of three different approaches to the tunneling wave function in quantum cosmology, clarifying boundary conditions and initial states.

Findings

All three approaches yield identical wave functions.

Scalar field fluctuations are well-behaved in all approaches.

Different boundary conditions are required for each method.

Abstract

The tunneling wave function of the universe is investigated in a minisuperspace framework of a de Sitter universe with a quantum scalar field, treated as a perturbation. We consider three different approaches to defining the tunneling wave function: (1) tunneling boundary conditions in superspace, (2) Lorentzian path integral, and (3) quantum tunneling from initial universe of a vanishing size. We show that the superspace approach requires Robin boundary conditions for the scalar field modes, the path integral approach requires adding an appropriate boundary term to the scalar field action, and the initial universe approach requires the initial quantum state of the scalar field to be Euclidean vacuum. We find that all three approaches yield identical wave functions and that scalar field fluctuations are well behaved, contrary to earlier claims in the literature.